I will discuss how the probability of getting a hemispherical power asymmetry in the CMB increases if the primordial fluctuations are non-Gaussian and extend to superhorizon scales. Interestingly, because of the scale-dependent nature of the power asymmetry, any non-Gaussianity postulated to increase the likelihood of obtaining such an asymmetry in the CMB data also increases the probability of a scale-dependent power spectrum modulation i.e. enhancement or suppression of power at large scales. Therefore, these large-scale ``anomalies'' that are observed in the CMB data can simply be consequences of the non-Gaussian cosmic variance in a universe larger than what we can observe, and not necessarily signals of a special scale or feature from the primordial era.